This Appendix extends stability selection with error control from [1]} to the randomised adaptive group Lasso.
With stability selection, variables are chosen according to their probabilities of being selected with some warranty on the selection error, [2]}. The first step consists in finding the probability of a variable \(k\)  of being selected under some data perturbation: let \(I_{b}\)  be one of \(B\)  random sub-samples of half the size of the training data drawn without replacement. For a given \(\lambda \)  an estimation of the probability of \(k\)  being selected is given by,
\(\hat{\Pi }^{\lambda }_{k} = \frac{1}{B}\sum _{b=1}^{B} \left\lbrace \begin{array}{ll}1 & \text{if } f_{k}^{\lambda }(I_b) > 0 \\0 & \text{otherwise}\end{array}\right.\) 
